Progressively censored schemes, in which experimentation is continually monitored from the onset, are advocated in some clinical trials and life testing problems with a view to early termination of the experiment, whenever feasible, and concomitant reduction in cost, time and sacrifice of lives of experimental subjects. Thus various stopping mechanisms of practical interest are describable in this framework. It is proposed to investigate the properties of such stopping rules in relation to sequential estimation and hypothesis testing problems in competing risk analyses where a particularly rich class of stopping times can be described. Likelihood ratio statistics applicable to the multi-risk model under progressive censoring are introduced and the properties of associated processes will be investigated in order to develop certain asymptotically pointwise optimal and asymptotically optimal policies in a Bayesian framework.